This is an issue to take up with individual website operators.

Almost every large website is going to be protected by both a CDN and an application firewall, either of which can be configured to slow down, gatekeep or outright block traffic coming from an IP that is suspected to be a VPN. And there are many reasons why they could be doing this:

• websites that rely on advertising to operate get less value from VPN users. A lot of users using the same IP address means advertisers have a more difficult time showing them relevant ads, thus paying the website less for them. So there is a financial incentive for a website to convince its users to stop using their VPN voluntarily.
• a security-minded site could be concerned with malicious actors using VPNs to shield their identities and locations during attack/breech attempts.
• a site seeking to protect its content from automated scraping by various bots (search crawlers, LLM data harvesting or competitors) may believe that those actors are using VPNs to hide their identities.

The only solution I can see is to reach out to the site operators themselves and explain your valid use case. I’ve done this a few times myself. I’ve never received a response, but some of the websites that I visit which used to block my VPN traffic eventually stopped blocking it.

If you don’t like something, make some noise.

Alternatively, you could use a cloud provider to spin up a micro instance running your own OpenVPN server that you re-roll IPs on occasionally, but this takes more effort and doesn’t really address the root cause.